A note on the genus of the HAWK lattice

Daniël M. H. van Gent

Paper 2025/215

A note on the genus of the HAWK lattice

Daniël M. H. van Gent

, Centrum Wiskunde & Informatica

Abstract

The cryptographic scheme and NIST candidate HAWK makes use of a particular module lattice and relies for its security on the assumption that finding module lattice isomorphisms (module LIP) is hard. To support this assumption, we compute the mass of the HAWK lattice, which gives a lower bound on the number of isometry classes of module lattices which cannot be distinguished from the HAWK lattice by an easily computed invariant called the genus. This number turns out to be so large that an attack based on the genus alone seems infeasible.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: HAWK Module lattice
Contact author(s): dmhvg @ cwi nl
History: 2025-02-13: approved; 2025-02-12: received; See all versions
Short URL: https://ia.cr/2025/215
License: CC0

BibTeX

@misc{cryptoeprint:2025/215,
      author = {Daniël M. H. van Gent},
      title = {A note on the genus of the {HAWK} lattice},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/215},
      year = {2025},
      url = {https://eprint.iacr.org/2025/215}
}